Summary: We solve the quartic Diophantine equation \(x^4+y^4=2z^4+2n^2w^4\), where \(n\) is a congruent number and find integer solutions \((x,y,z,w)\) with \(xyzw\neq 0\). We also show that the rational points of this equation are dense in both Zariski and real analytic topology. Finally, the existence of a steady relation between Kummer surfaces and congruent numbers is asserted.